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/*
* ***** BEGIN GPL LICENSE BLOCK *****
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* The Original Code is Copyright (C) 2015 by Blender Foundation.
* All rights reserved.
*
* The Original Code is: all of this file.
*
* ***** END GPL LICENSE BLOCK *****
* */
/** \file blender/blenlib/intern/math_statistics.c
* \ingroup bli
*/
#include "MEM_guardedalloc.h"
#include "BLI_math.h"
#include "BLI_utildefines.h"
#include "BLI_strict_flags.h"
/********************************** Covariance Matrices *********************************/
/**
* \brief Compute the covariance matrix of given set of nD coordinates.
*
* \param n the dimension of the vectors (and hence, of the covariance matrix to compute).
* \param cos_vn the nD points to compute covariance from.
* \param nbr_cos_vn the number of nD coordinates in cos_vn.
* \param center the center (or mean point) of cos_vn. If NULL, it is assumed cos_vn is already centered.
* \param use_sample_correction whether to apply sample correction
* (i.e. get 'sample varince' instead of 'population variance').
* \return r_covmat the computed covariance matrix.
*/
void BLI_covariance_m_vn_ex(
const int n, const float *cos_vn, const int nbr_cos_vn, const float *center, const bool use_sample_correction,
float *r_covmat)
{
int i, j, k;
/* Note about that division: see https://en.wikipedia.org/wiki/Bessel%27s_correction.
* In a nutshell, it must be 1 / (n - 1) for 'sample data', and 1 / n for 'population data'...
*/
const float covfac = 1.0f / (float)(use_sample_correction ? nbr_cos_vn - 1 : nbr_cos_vn);
memset(r_covmat, 0, sizeof(*r_covmat) * (size_t)(n * n));
#pragma omp parallel for default(shared) private(i, j, k) schedule(static) if ((nbr_cos_vn * n) >= 10000)
for (i = 0; i < n; i++) {
for (j = i; j < n; j++) {
r_covmat[i * n + j] = 0.0f;
if (center) {
for (k = 0; k < nbr_cos_vn; k++) {
r_covmat[i * n + j] += (cos_vn[k * n + i] - center[i]) * (cos_vn[k * n + j] - center[j]);
}
}
else {
for (k = 0; k < nbr_cos_vn; k++) {
r_covmat[i * n + j] += cos_vn[k * n + i] * cos_vn[k * n + j];
}
}
r_covmat[i * n + j] *= covfac;
}
}
/* Covariance matrices are always symetrical, so we can compute only one half of it (as done above),
* and copy it to the other half! */
for (i = 1; i < n; i++) {
for (j = 0; j < i; j++) {
r_covmat[i * n + j] = r_covmat[j * n + i];
}
}
}
/**
* \brief Compute the covariance matrix of given set of 3D coordinates.
*
* \param cos_v3 the 3D points to compute covariance from.
* \param nbr_cos_v3 the number of 3D coordinates in cos_v3.
* \return r_covmat the computed covariance matrix.
* \return r_center the computed center (mean) of 3D points (may be NULL).
*/
void BLI_covariance_m3_v3n(
const float (*cos_v3)[3], const int nbr_cos_v3, const bool use_sample_correction,
float r_covmat[3][3], float r_center[3])
{
float center[3];
const float mean_fac = 1.0f / (float)nbr_cos_v3;
int i;
zero_v3(center);
for (i = 0; i < nbr_cos_v3; i++) {
/* Applying mean_fac here rather than once at the end reduce compute errors... */
madd_v3_v3fl(center, cos_v3[i], mean_fac);
}
if (r_center) {
copy_v3_v3(r_center, center);
}
BLI_covariance_m_vn_ex(3, (const float *)cos_v3, nbr_cos_v3, center, use_sample_correction, (float *)r_covmat);
}
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